For the beginning, we study the problem to be solved by the present invention as well as the solutions of the prior art. When a cold glass sheet is moved into a hot furnace the temperature of which exceeds 700.degree. C. and which is fitted with rollers, the glass initially curves vigorously, so that the edges of glass rise upwards. This phenomenon is quite natural with the rollers emitting heat to the glass at a quicker rate than that received by glass from the top portion of the furnace. The main reason for this phenomenon is the rollers carrying and conveying the glass. The rollers conduct heat to glass by contacting it and, on either side of the point of contact, there is a relatively wide zone in which the roller is very close to the glass, whereby heat is transferred by conduction through a medium (air). It can be calculated that, if a furnace contains rollers at 120 mm relative distances and the diameter of the rollers is approximately 95 mm, the heat flow being transferred from such a roller track through conduction exceeds that emitted from an analogous plane surface which would lie at a distance of 3 mm from the glass. In the furnace conditions, this corresponds to a heat transfer coefficient of approximately 20 W/m2.degree. C.
A drawback caused by this initial curving is that the central portion of glass warms up considerably faster than the edges which may result in a serious optical error as a long stripe in the central portion of the glass where the only point of contact with rollers has been.
In addition, the rollers also leave marks in the same portion of glass resulting in a completely useless sheet of glass. The reason for such marks is naturally the fact that the linear support of rollers is applied to an extremely narrow portion in the central of glass so that the surface structure of the glass tends to become fractured or grated.
In the following study the transfer of heat to the glass has been divided into three components: radiation, conduction and convection, since this is the only way to readily explain the above-mentioned detrimental phenomenon in a heating furnace. As from above the glass, the heat primarily transfers through radiation and convection, the share of conduction heat is so insignificant that it can be ignored in the study.
The situation is different on the bottom surface of the glass since, in addition to radiation, there is a very strong conduction heat flow. The share of convection in the heat transfer is very hard to evaluate but, compared to conduction, it is definitely very small.
On the basis of a rough preliminary study of the behavior of these three forms of heat transfer in the heating step, it is possible to note that they differ considerably from each other:
I Radiation PA0 II Conduction and convection
It is well-known that radiation heat follows the formula derived from Stefan-Bolzmann law: EQU q.sub.s =.epsilon..sub.1 .multidot..epsilon..sub.2 .multidot..sigma..multidot.(T.sub.1.sup.4 -T.sub.2.sup.4)
.epsilon..sub.1 =emission coefficient of a heat source (semi-space) PA1 .epsilon..sub.2 =emission coefficient of a heat receiver PA1 .sigma.=Stefan-Bolzmann constant (5,67 W/m2(100.degree. K.).sup.4) PA1 T.sub.1 =temperature of a heat source (semi-space) PA1 T.sub.2 =temperature of a heat receiver PA1 q.sub.s =radiation energy (W/m2) PA1 .epsilon..sub.1 .multidot..epsilon..sub.2 =.epsilon.whose value when heating glass is about 0,6 PA1 g.sub.j =heat flow (W/m2) PA1 .lambda.=heat conductivity of gas (thin layer) PA1 T.sub.1 -T.sub.2 =temperature difference PA1 a=distance of conduction PA1 1.1. The service life of the rollers is relatively short; in a continuous 3-shift work just one to three years. PA1 1.2. As the rollers require a steel core with their well-kown creep properties, in a while the roller starts to "play" due to eccentricity. PA1 1.3. Marks are easily formed in the center of the glass due to initial curving. PA1 1.4. Warming up of the glass is very uneven, since the leading edge is capable of cooling the roller drastically and the central portion and the glass, which forms the trailing edge at any given time, warm up less. As the glass moves back and forth, the center remains much colder than the ends of the glass with the result that quality is poor and the glass fractures easily in tempering. PA1 1.5. Cooling of the roller very much depends on the size and thickness of glass making the heat control difficult. PA1 1.6 It is a general rule that the glasses must be washed after the tempering as a result of asbestos dust. PA1 s=thickness of glass PA1 .lambda.=heat conductivity of glass
In diagrams 1 and 2, curves B and D illustrate the radiation heat flows calculated from the above formula with emission coefficient of .epsilon.=0,6, when the temperature of a particular emitting semispace is either 720.degree. C., 700.degree. C. or 670.degree. C. (993.degree. K., 973.degree. K., or 943.degree. K.) and temperature of the heating glass is the other variable.
It can be noted from the diagrams that heat transfer does not change very quickly at the early stages of heating even though the glass temperature rises. On the other hand, towards the end, the heating effect drops very steeply. As a matter of fact, the heat transfer coefficient increases all the time as the glass is heated.
On the basis of the foregoing, it is evident that, when trying to explain the behavior of glass in the furnace during heating, it is not possible to use any constant as heat transfer coefficient but the case must be illustrated with a diagram as we have done in this specification.
Conduction is calculated from the formula: EQU g.sub.j =.lambda.(T.sub.1 -T.sub.2)/a
In this case, the heat transfer coefficient is nearly constant, i.e. independent of the glass temperature. A minor change naturally occurs for the reason that, when the glass enters the furnace, the mean value of temperature between the rollers and glass is approximately 350.degree. C. and when the glass leaves the furnace, the corresponding mean value is about 650.degree.-670.degree. C. Thus, the heat conductivity of air varies in the range of 0,048-0,064 W/m.degree.C. which, relatively speaking, is a minor change since heat transfer through conduction is relatively small towards the end of the heating.
Diagram 1 of the drawings illustrates the heat transfer effect from furnace to glass. In diagram 1, conduction and convection have been combined for both above and below the glass heating. In both cases, the heat transfer coefficient has been presumed to be constant since, from above the glass, the convection heat flow is small anyway and the conduction heat flow of the lower side is of such a nature that it very closely depends only on the temperature difference. To be quite accurate, the conduction heat flow demonstrator C should be slightly upwardly curved the same way as heat radiation, and demonstrator A of the free convection heat flow should, on the contrary, be slightly downwardly curved.
The following methods are known for the prevention of the blending of glass or the drawbacks caused thereby:
1. The use of asbestos rollers or other corresponding fiber materials whose heat storage ability is small in view of the volume and whose heat conductivity is as small as possible. The basic idea of this procedure is that, with heat being first emitted quickly, the surface temperature of the roller decreases causing a vigorous change primarily in the radiation energy. This can be clearly noted by comparing demonstrators B and D in diagram 1, the former corresponding to the temperature of 720.degree. C. and the latter to the temperature of 670.degree. C. Later on, as the glass is warming up, the furnace will be capable of emitting more heat to the roller than the amount taken up by the glass, the temperature of the roller surface returning to its initial value which during loading is practically always lower than temperature of the furnace.
In such furnaces, the glass also initially bends very vigorously the edges upwards followed by relative quick straightening as a result of cooling of the rollers.
The use of such rollers, however, leads to some very detrimental characteristics:
2. The rollers ae mounted further away from each other (fewer rollers). The detrimental heat conduction of the bottom side is practically directly proportional to the roller density, so the drawback can thus be diminished as far as the curving is concerned but, on the other hand, a lot more serious hazard emerges: the glass will be corrugated. If we consider the glass to be a sheet resulting on brackets, the bending stresses in the sheet, which stresses in fact represent the tendence of glass to become corrugated in soft condition, are directly proportional to the square of the distance between said rollers. Such corrugation in glass is one of the worst problems in horizontal tempering plants provided with roller support and thus, in practice, there is no chance at all to extend the distance between rollers.
3. Making the heating system of very small mass and quickly regulated. In this case, the basic idea is to compensate the powerful conduction heat flow with a corresponding heat effect from above the glass. A drawback in such an arrangement is the high price and complexity of the system, since it is necessary to anticipate in which part of the furnace the glass is travelling. Another, and a more detrimental, factor is the fact that, in any case, the heating system is to a certain degree slow, the control of temperatures in the furnace being difficult and, particularly with varying furnace loads, the control is next to impossible. Even this system does not eliminate the initial bending of glass but only cuts down its duration.
4. The length of a stroke is extended to be more than the longest glass load and the lower side heating is eliminated. The idea here is to decrease temperature of the rollers, whereby radiation energy, in particular, rapidly decreases. In practice, this alternative, the same way as alternative 3, requires very accurately controlled loading of the glasses and, hence, the load of the furnace. Temperature of the rollers immediately tends to equalize itself with that of the furnace if, for some reason, just one loading is omitted. To maintain temperature of the rollers quite low with respect to that of the furnace is really a hard task which can only be successfully achieved with the help of long experience and a lot of automatic data processing.
The worst drawback in this system is that bending of the glass with the edges upwards is indeed initially reduced but, correspondingly, towards the end of the heating said edges bend downwards, which means that the bending itself has not been eliminated but divided into two phases, so that bending in both directions is practically the same. The fact that, in the end, the glass bends with the edges downwards is indeed catastrophic in view of the service life of the roller, since the sharp edges bumping against the rollers cause indentations and scratches, especially when tempering thick glasses.
Before studying the solution of the present invention for the prevention of glass bending and the drawbacks caused thereby, we will examine the physical basis of glass bending. If we think of said glass as a sheet whose various surface sections receive their own heat flow at the heating stage, the heat flow which passes through the glass is the one that tends to equalize the heat flows of various intensities coming from outside. If we disregard the initial situation and transition period, which is a short period only, it can be said that, with normally temperable glass thicknesses, the final temperature difference will be reached in less than 10 seconds. Temperature difference between the surfaces approaches the limit value: ##EQU1## .DELTA.T=temperature difference .DELTA.q=difference of heat flows to opposite surfaces
The change of temperature within the glass is not linear but a second degree curve. However, the bending caused by this temperature difference can be calculated without essential error aes if the change were linear. (In practice, the glass bends moe than the bending calculated with linear temperature change.) Thus, the radius, according to which the glass curves, is obtained from the following formula: ##EQU2## R=radius of curvature .alpha.=coefficient of heat transfer
When the bending is slight as compared to the length of the glass, value of the bending is obtained from the formula: ##EQU3## .delta.=bend L=the length of glass corresponding to bend
The approximation formula, which illustrates bending of the glass depending on the difference between the heat flows received by the glass from different sides, is finally obtained by incorporating the temperature difference formula (1) in the bend formula (3). ##EQU4##
In the normally used flat glass .alpha..apprxeq.8,7.multidot.10.sup.-6 1/.degree.C. and .lambda.1 W/m..degree.C. If it is further presumed that L=1 m and .DELTA.q=1,0 kW/m2, the following formula will be obtained: ##EQU5##
In other words, we can assume as a rough rule that the bend for the length of 1 meter will be approximately 0,5 mm, when the difference between the heat flows received by the glass from various sides is 1,0 kW/m2. The bend is independent of the thickness of glass.